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Stanley's theorem states that the total number of 1s that occur among all unordered partitions of a positive integer is equal to the sum of the numbers of distinct members of ...

The eight Gell-Mann matrices lambda_i, i=1,...,8, are an example of the set of generators of the Lie algebra associated to the special unitary group SU(3). Explicitly, these ...

The integer sequence 1, 0, 1, 1, 2, 1, 3, 2, 4, 3, 5, 4, 7, 5, 8, 7, 10, 8, 12, 10, 14, 12, 16, 14, 19, 16, 21, 19, ... (OEIS A005044) given by the coefficients of the ...

A group action G×Omega->Omega might preserve a special kind of partition of Omega called a system of blocks. A block is a subset Delta of Omega such that for any group ...

Every finite Abelian group can be written as a group direct product of cyclic groups of prime power group orders. In fact, the number of nonisomorphic Abelian finite groups ...

Let a closed interval [a,b] be partitioned by points a<x_1<x_2<...<x_(n-1)<b, where the lengths of the resulting intervals between the points are denoted Deltax_1, Deltax_2, ...

A Steiner quadruple system is a Steiner system S(t=3,k=4,v), where S is a v-set and B is a collection of k-sets of S such that every t-subset of S is contained in exactly one ...

Elder's theorem is a generalization of Stanley's theorem which states that the total number of occurrences of an integer k among all unordered partitions of n is equal to the ...

A multiplication table is an array showing the result of applying a binary operator to elements of a given set S. For example, the following table is the multiplication table ...

Smarandache sequences are any of a number of simply generated integer sequences resembling those considered in published works by Smarandache such as the consecutive number ...